Learning about passivity from data

TL;DR

The paper tackles the problem of identifying a storage function for passive systems directly from data, avoiding reliance on a detailed model. It proposes a data-driven approach that parameterizes the storage function as $S(x)=\theta^T\phi(x)$ and recovers $\theta$ via a linear program that enforces passivity constraints over collected input/state/output data, with a windowing parameter $T$ to mitigate noise. The method is demonstrated on a pendulum benchmark, recovering a storage function close to the theoretical one and showing robustness to noise when using larger windows; it also demonstrates several passivity-based tasks, including feedback certification, estimation of $L_f S$, DoA estimation, and damping control, all without full system identification. The approach provides a practical, model-free framework for passivity analysis and controller design, with potential applicability to a wide range of nonlinear systems where the model is uncertain or unavailable.

Abstract

This paper presents a data-driven methodology to estimate the storage function of a passive system. The methodology consists in parametrizing the storage function with a dictionary then running a linear program. Results on a benchmark are presented to illustrate its properties, including its robustness to noise. Various uses of the storage function that do not require knowledge of a model are also discussed.

Figures (2)

• Figure 1: Phase-plot of the system that form the data set
• Figure 2: Levels curves of the estimated Storage function $\hat{S}(\mathbf{x} )$